Environmental Research 146 (2016) 308–314

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Bayesian estimation of the dynamics of pandemic (H1N1) 2009 influenza transmission in Queensland: A space–time SIR-based model Xiaodong Huang a, Archie C.A. Clements b, Gail Williams c, Kerrie Mengersen d, Shilu Tong a, Wenbiao Hu a,n a School of Public Health and Social Work, Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Queensland, Australia b Research School of Population Health, The Australian National University, Canberra, ACT, Australia c School of Public Health, the University of Queensland, Brisbane, Queensland, Australia d Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia

art ic l e i nf o

a b s t r a c t

Article history: Received 11 September 2015 Received in revised form 10 December 2015 Accepted 11 January 2016

Background: A pandemic strain of influenza A spread rapidly around the world in 2009, now referred to as pandemic (H1N1) 2009. This study aimed to examine the spatiotemporal variation in the transmission rate of pandemic (H1N1) 2009 associated with changes in local socio-environmental conditions from May 7–December 31, 2009, at a postal area level in Queensland, Australia. Method: We used the data on laboratory-confirmed H1N1 cases to examine the spatiotemporal dynamics of transmission using a flexible Bayesian, space–time, Susceptible-Infected-Recovered (SIR) modelling approach. The model incorporated parameters describing spatiotemporal variation in H1N1 infection and local socio-environmental factors. Results: The weekly transmission rate of pandemic (H1N1) 2009 was negatively associated with the weekly area-mean maximum temperature at a lag of 1 week (LMXT) (posterior mean:  0.341; 95% credible interval (CI):  0.370–  0.311) and the socio-economic index for area (SEIFA) (posterior mean:  0.003; 95% CI:  0.004–  0.001), and was positively associated with the product of LMXT and the weekly area-mean vapour pressure at a lag of 1 week (LVAP) (posterior mean: 0.008; 95% CI: 0.007– 0.009). There was substantial spatiotemporal variation in transmission rate of pandemic (H1N1) 2009 across Queensland over the epidemic period. High random effects of estimated transmission rates were apparent in remote areas and some postal areas with higher proportion of indigenous populations and smaller overall populations. Conclusions: Local SEIFA and local atmospheric conditions were associated with the transmission rate of pandemic (H1N1) 2009. The more populated regions displayed consistent and synchronized epidemics with low average transmission rates. The less populated regions had high average transmission rates with more variations during the H1N1 epidemic period. & 2016 Elsevier Inc. All rights reserved.

Keywords: Pandemic (H1N1) 2009 influenza Susceptible-Infected-Removed model Spatial conditional autoregressive model Transmission rate

1. Introduction Influenza infection causes extensive morbidity and mortality in the human population every year (Earn et al., 2002; Simonsen et al., 1997; Thompson et al., 2003), with annual influenza epidemics leading to approximately 250,000–500,000 deaths through the year globally (WHO, 2014). In 2009, a pandemic influenza A H1N1 virus spread rapidly around the world, now referred to as pandemic (H1N1) 2009. By January 3, 2010, more than 12,799 deaths associated with pandemic (H1N1) 2009 had been n

Corresponding author. E-mail address: [email protected] (W. Hu).

http://dx.doi.org/10.1016/j.envres.2016.01.013 0013-9351/& 2016 Elsevier Inc. All rights reserved.

reported (WHO, 2010). Pandemic (H1N1) 2009 emerged in Australia and the first laboratory-confirmed infections were confirmed on May 8, 2009 in the state of Queensland (Baker et al., 2011). By January 1, 2010, there were 37,553 confirmed cases of pandemic (H1N1) 2009 and 191 deaths in Australia (Australian Government Department of Health and Ageing, 2010). Previous studies have examined the relationship between weather and socio-ecological factors and incidence of pandemic (H1N1) 2009 transmission (Earn et al., 2012; Gog et al., 2014; Hu et al., 2012)of pandemic (H1N1) 2009 transmission, and have estimated reproductive number (R0) to describe the intensity of transmission risk of pandemic (H1N1) 2009 using mathematical (susceptible-infectious-recovered (SIR)) models (He et al., 2013a; Paine et al., 2010; Towers and Feng 2009). A study of pandemic

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(H1N1) 2009 transmission in Canada firstly investigated the weather effects on the transmission rate using aggregated cases at each province, and found that simulation from transmission rates incorporating weather factors was much better than simulation without weather factors (He et al., 2013a). However, few reports have explored the association between local transmission rate of pandemic (H1N1) 2009 and local socio-environmental conditions, although influenza transmission has often been linked to weather and socio-ecological factors (Fuhrmann, 2010; Murray et al., 2006; Van Noort et al., 2012), and few have examined patterns of transmission rate of pandemic (H1N1) 2009 over time and space, even though infectious disease transmission requires close spatial and temporal proximity between infectious and susceptible people. Characterising recent pandemics is informative for development of effective and cost-effective interventions to deal with future pandemics (Bootsma and Ferguson, 2007; Eggo et al., 2011; He et al., 2013b). A better understanding of the spatiotemporal dynamics of pandemic (H1N1) 2009 is critical to designing effective control strategies to minimise the spread of future influenza pandemics, as well as help to establish early warning systems (Fuhrmann, 2010). In this study, a Bayesian approach with the combination of a SIR model and a spatial conditional autoregressive (CAR) model was used to understand the transmission of pandemic (H1N1) 2009 over time and space after accounting for the effect of local weather conditions, socio-ecological factors and spatiotemporal variability, using data on laboratory-confirmed pandemic (H1N1) 2009 cases across Queensland, Australia.

2. Materials and methods 2.1. Study site and data collection The study area was Queensland, the second-largest state in Australia, which is located in the north-east of the country. Due to its large area, there is significant variation in climate across the state: low precipitation and hot summers occur in the inland west; a monsoonal climate occurs in the north; warm temperate conditions occur on the coastal regions; and low minimum temperatures occur in the south-east inland areas (Australian Government Bureau of Meteorology, 2014). The population of Queensland was 4,332,739 at the 2011 Census, making it the thirdmost populous state in Australia (Australian Bureau of Statistics, 2013a). Data on the numbers of weekly laboratory-confirmed H1N1 cases for each postcode area were obtained from Queensland Health for the period of May 7, 2009 to December 31, 2009 across the state. Data on population size and socio-economic index for area (SEIFA) for each postal area were obtained from the Australian Bureau of Statistics. SEIFA is a continuous variable and summarizes average socio-economic characteristics, including education, occupation and wealth, and can be used to describe the distribution of social and economic well-being across different regions (Australian Bureau of Statistics, 2013b). Data on monthly daily maximum temperature (°C) and monthly daily vapour pressure (hPa) for each region were obtained from the National Computational Infrastructure between 1st May and 31st December 2009 (National Computational Infrastructure, 2014). 2.2. Data analysis A Bayesian space–time SIR model was developed to assess the spatiotemporal variability of transmission rate of pandemic (H1N1) 2009 after accounting for the effects of socio-environmental factors, the transmission dynamics of the pathogen and spatial correlation in the data. We denoted the first study week as


starting from May 7, 2009. Cases were attributed to weeks based on reported onset date, although the first laboratory-confirmed H1N1 case in Australia was announced on May 8, 2009 in Queensland. Let yij be weekly laboratory-confirmed H1N1 cases in region i and week j, (i¼1,…, 424; j¼1,…, 34). A discrete form SIR model for the size of susceptible population at week (jþ1) and region i is given by Si, j + 1 = Si, j − Ii, j , where S and I represent numbers in the susceptible and infected populations, respectively. The number of the infected cases in region i and week j was assumed to have a Poisson distribution, with expected number given by a function of the number of infected cases in week (j 1) and the susceptible population size in week j. Hence, Iij ~Pois(μij ), and μij is given by (Lawson and Song, 2010):

μij = βij × Sij × Ii, j − 1


log(μij ) = log(βij ) + log(Sij ) + log(Ii, j − 1); log(βij ) = b 0+b1 × (LMXT )i, j − 1 + b2 × (SEIFA)i + b3 × (LMXT )i, j − 1 × (LVAP )i, j − 1 + ui + vi (2) Here b ¼(b0, b1, b2, b3) is the vector of regression coefficients for the intercept (representing the log-transformed baseline transmission rate across all locations), mean maximum temperature at a lag of 1 week (LMXT), SEIFA and LMXT* (log-transformed mean vapour pressure at a lag of 1 week (LVAP)), respectively; ui corresponds to structured (spatial) heterogeneity and represents spatial variation in transmission rate between regions that captures the effects of unobserved variables with an underlying spatial pattern; vi correspond to geographically unstructured (i.e. random effect) heterogeneity in the transmission rate; and βij is the weekly transmission rate at region i and week j after incorporating the spatiotemporal effects of local social-environmental factors, the transmission dynamics of pandemic (H1N1) 2009 (i.e. SIR model) and random effects (ui and vi). A CAR model was applied to model spatial dependency by the random effect ui (Besag et al., 1995; Lawson, 2013). This approach models the effect of proximity using a first-order neighbourhood structure, whereby the random effect is assumed to have a normal distribution, with the conditional weighted mean given by the average of the neighbours. Moreover, the model only examined the one-week lagged relationship between transmission rate and weather factors due to the short time of mean duration of H1N1 infectiousness. Additionally, we assumed Si1 ¼ 65% of population size for each region at the first study week (Dorigatti et al., 2013; He et al., 2013a). In general, surveillance data do not include all influenza cases over time and space during a pandemic period (Reed et al., 2009), so it was impractical to obtain the entire set of infected cases (Iij) of pandemic (H1N1) 2009. Instead, we used the data on weekly laboratory-confirmed H1N1 cases (yij) to estimate the epidemiological dynamics of pandemic (H1N1) 2009 in this study. All covariate coefficients had diffuse normal priors, given by b  N (0.0, 1.0E6). The variances of the random effects had uniform priors, su  U(0,5) and sv  U(0,5). In the study, we assumed LMXT as the main effect on H1N1 transmission. Because LMXT and LVAP were strongly correlated, we included the product of LMXT and LVAP in the model to reduce the bias of collinearity, and took into account the effect of LVAP. Four models were considered, including the full model as described in Eq. (2) and three reduced models that were developed to determine which random effects (u and v) provided the best fit, or whether the spatial model was appropriate to describe H1N1 transmission, briefly: 1) Model 1 had two random effects, i.e. as described in equations (2); 2) Model 2 had a random effect ui only; 3) Model 3 had a random effect vi only; and 4) Model 4 had


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no random effects, i.e. ui ¼vi ¼0 in Eq. (2). A comparison of model fit was performed using the deviance information criterion (DIC). Posterior distributions for parameters of interest were obtained through Markov chain Monte Carlo (MCMC) sampling and these were summarised using means, standard deviations and quantiles. Convergence was assessed by checking the trace and the autocorrelation plots for the sample chains. We ran 150,000 MCMC iterations and discarded the first 50,000 MCMC iterations as burnin. The Bayesian analysis was performed using WinBUGS software version 1.4.

3. Results Table 1 shows the summary statistics for all variables. Patients were aged 0–109 years, and most (61.3%) were aged 10–40 years. The largest number of laboratory-confirmed cases of pandemic (H1N1) 2009 was identified in July 2009. Fig. 1 shows the spatial distribution of observed mean weekly H1N1 incidence, with higher incidence detected in north and central Queensland. There were three postal areas that experienced the highest observed weekly mean incidence during the study period, including a postal area in Central Queensland with an observed mean incidence of 115.38 per 1000 population, a postal area in Townsville with an observed mean incidence of 91.28 per 1000 population and a postal area in the Torres Strait and Northern Peninsula with an observed mean incidence of 41.92 per 1000 population during the epidemic period. In Table 2, the DIC values for the four models indicated that Model 1 had a better fit than the other models. This implies that there was substantial spatiotemporal variation in H1N1 risk across Queensland during the study period, after accounting for LMXT, SEIFA and the interactive effect, with high spatially structured residual risk particularly evident in Central West Queensland, North West Queensland and South West Queensland (Fig. 2). From Model 1 (Table 3), it was estimated that weekly transmission rate was strongly negatively associated with local LMXT and local SEIFA, and was stronly positively related to LMXT*LVAP. The results also indicated that the effect of LMXT on H1N1 transmission was varied and associated with the magnitude of LVAP (i.e., (0.341  0.008LVAP)*LMXT). Fig. 3 indicates that there were differences in the spatial variation in posterior mean weekly transmission rate (βij) per 100,000 population during the early epidemic period (week 4), peak epidemic period (week 9) and epidemic decline period (week 25). Posterior mean weekly transmission rate was highest in north western, central western and south western Queensland in week 9. When the posterior means of log(βij) were aggregated by local population groupings, Fig. 4 shows the average of the posterior means log(βij) with 95% credible intervals for varying grouped population sizes across Queensland. The average of the posterior means for small grouped population sizes was large and more variable. Increasing the grouped population size tended to decrease the average of the posterior means, tending to a more constant rate during the epidemic period in Queensland. Table 1 Summary statistics for all variables during 1st May–31st December 2009 in Queensland. Variable



Percentiles 25



Local SEIFA 953.2 126.6 913.3 951.5 999.8 Weekly H1N1cases 353.5 677.6 1.0 20.5 311.3 Weekly vapour pressure (hPa) 14.76 4.07 11.81 14.13 17.25 Weekly maximum temperature (°C) 26.4 4.3 23.3 26.5 29.6

Fig. 1. The spatial distribution of mean weekly incidences of observed laboratoryconfirmed cases for pandemic (H1N1) 2009 during the period of 7th May 2009 to 31st December 2009 across Queensland.

Table 2 Model comparisons for H1N1 cases in Queensland during 7th May–31st December, 2009, using the DIC criterion. Model


1 A Bayesian space–time SIR-based model

LMXTa, SEIFAb, ud, ve










2 A Bayesian space–time SIR-based model 3 A Bayesian space–time SIR-based model 4 A Bayesian SIR-based model


Random effect DIC


LMXT: mean maximum temperature at a lag of one week. SEIFA: socio-economic indexes for area. c LMXT*LVAP: the product of LMXT and LVAP. LVAP represented log-transformed vapour pressure at a lag of 1 week. d u: structured heterogeneity. e v: unstructured heterogeneity. b

Fig. 5 depicts the distribution of the growth slope coefficients of the relationships between estimated posterior mean weekly transmission rates and week (from the epidemic week 2–week 9), and the distribution of the decline slope coefficients of the relationship between estimated posterior mean weekly transmission rate and week (from the peak week 10 – the end of the first wave week 25) in the linear regression models (i.e. βij ¼ α0i þ αi  (week)j) over local population sizes. The slope coefficients (αi) were more heterogeneity for smaller population. The speeds of the H1N1 epidemic growth and decline were faster in the regions with small and moderate population sizes than these in the regions with large population sizes (Fig. 5).

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Fig. 2. The spatial distribution of posterior mean of structured and unstructured heterogeneity random effects during the study period.

Table 3 Posterior means and 95% credible intervals of parameters for Model 1. Parameter



95% Credible interval


 0.164  0.341  0.003 0.008

0.638 0.015 6.076E  4 5.198E  4

 1.567 to1.000  0.370 to  0.311  0.004 to  0.001 0.007–0.009

4. Discussion Our study showed that there was a significant negative relationship between transmission rate and LMXT. An increase in maximum temperature was associated with a decrease in incidence of pandemic (H1N1) 2009 in previous studies (Hu et al., 2012; Sirisena and Noordeen, 2014). Growing evidence has demonstrated that influenza transmission is strongly related to temperature (Barreca and Shimshack, 2012; Fuhrmann, 2010; Lowen et al., 2007). Cold and dry weather conditions are more likely to favour influenza transmission because such conditions can enhance the survival of the influenza virus (Lowen et al., 2007; Polozov et al., 2008). On the other hand, a strong positive effect of LMXT*LVAP on transmission rate was observed in the study. The combined effect of –(0.341  0.008LVAP)*LMXT showed that increasing LVAP and decreasing LMXT may be associated with an increase in transmission rate. Influenza transmission is mostly related to droplet transmission and airborne transmission (Weinstein et al., 2003). High evaporation has been associated with increased the risk of long-range transmission (Tang et al., 2006). SEIFA was also negatively associated with the transmission rate of pandemic (H1N1) 2009 in the study. A high SEIFA score typically reflects a better social and economic well-being in a given region. The high H1N1 risks in the regions with low SEIFA scores might reflect that there were more vulnerable people with lower education, fewer local control resources and insufficient local health services in these lower socio-economic status areas. There were distinct differences in spatiotemporal distributions of the posterior mean weekly transmission rate during the

different epidemic periods across Queensland. Extensive clusters of high weekly transmission rates of pandemic (H1N1) 2009 appeared during the epidemic growth and peak period. Discrete clusters of high risk of pandemic (H1N1) 2009 appeared during the period of the epidemic decline. The maps of the posterior means of random effects, which might capture variation in the outcome due to the effects of unobserved covariates, showed greater values mainly in North West Queensland, Central West Queensland and South West Queensland (Fig. 2) where there are high proportion of indigenous population or remote communities (Baker et al., 2011; Queensland Government, 2011). This result might be supported by previous studies that reported indigenous populations were among the most vulnerable to poor outcomes for pandemic (H1N1) 2009 globally (Bishop et al., 2009). Their high risk might be explained by higher prevalence of co-morbidities such as obesity, diabetes and chronic respiratory disease, and poor living conditions (Baker et al., 2009; La Ruche et al., 2008), as are found in indigenous communities in North Queensland and rural remote regions (Queensland Health, 2011). We suggest that rural and indigenous communities might need to be the target of enhanced epidemic surveillance in the next influenza pandemic. There was more heterogeneity among the posterior mean weekly transmission rates in the regions with smaller population sizes during the H1N1 epidemic period (Figs. 4 and 5). The most populous regions displayed lower average of the posterior mean transmission rate and consistent and synchronized epidemics. The speed of the H1N1 epidemic growth and decline was also heterogeneous among areas with different population sizes across Queensland. A previous study found that spread of influenza was associated with population size and less populated regions showed more variation in transmission patterns (Viboud et al., 2006). Another study of pandemic (H1N1) 2009 in Mexico also observed that low population regions had higher morbidity rate than large population regions but this did not relate to bias in local age structure and testing practices (Chowell et al., 2011). This study supported the findings of previous studies and also revealed that regions with smaller populations were more likely to be sensitive to pandemic (H1N1) 2009 in Queensland.


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Fig. 3. The spatiotemporal distribution of posterior mean weekly transmission rate of pandemic (H1N1) 2009 during the three epidemic weeks.

Fig. 4. The average of posterior mean log(βij) with credible intervals was plotted against the grouped population size during the study period across Queensland.

Fig. 5. Estimated growth slope coefficients (from epidemic week 2–week 9) and decline slope coefficients (from the peak week 10–the end of the first wave week 25) for posterior mean weekly H1N1 transmission rates were plotted against population size during the H1N1 epidemic period across Queensland.

A limitation of the present study was that laboratory-confirmed H1N1 cases would not have included the entire number of infected people during the epidemic period as many people would have

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had mild infections and not sought medical care. This might have led to underestimating the transmission rate and H1N1 risk. However, it was plausible that there should be a strong positive linear relationship between the number of weekly infected cases and the number of weekly laboratory-confirmed cases. Hence, for the purpose of the study, the data on laboratory-confirmed H1N1 cases were assumed to mirror the relative magnitude of pandemic (H1N1) 2009 over space and time. Additionally, the study may have faced the usual problems of an ecological design. For example, other social factors (human behaviour) and weather factors (e.g., humidity and minimum temperature) may influence H1N1 virus transmission. Incorporating these factors may more comprehensively explain spatiotemporal variations in H1N1 incidence and better predict the transmission of H1N1 virus in the future. However, such data were not available at the time of this study. Maps of the spatiotemporal variability of transmission rates can assist in health management and enable more efficient use of control resources in future influenza pandemics. For example, health officials and policy makers may pay more attention to low SEIFA regions, where they may provide more health education and health services during an epidemic period. Our findings might guide the future mobilisation and targeting of vaccines to the different regions. This study also identified spatial patterns in influenza risk, which might provide useful clues to other potential factors related to the clustering of H1N1.

5. Conclusion This study has determined local maximum temperature, local vapour pressure and SEIFA as driving factors of transmission of pandemic (H1N1) 2009. There was substantial spatiotemporal variation in the transmission rate of pandemic (H1N1) 2009 in different postal areas across Queensland. The more populated regions displayed consistent and synchronized epidemics. There were high variations in the posterior mean weekly transmission rate in the regions with smaller population sizes during the H1N1 epidemic period. This approach allowing for spatial dependence and susceptible-infected–recovered dynamics can improve identification of clusters of the transmission risk of pandemic (H1N1) 2009, that could help local health authority to design effective control strategies to minimise the spread of future influenza pandemics.

Acknowledgements We thank the Queensland Department of Health, Australian Bureau of Meteorology, and Australian Bureau of Statistics for providing the data on laboratory-confirmed H1N1 cases, climate and population growth, respectively.

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Bayesian estimation of the dynamics of pandemic (H1N1) 2009 influenza transmission in Queensland: A space-time SIR-based model.

A pandemic strain of influenza A spread rapidly around the world in 2009, now referred to as pandemic (H1N1) 2009. This study aimed to examine the spa...
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